Question

sinα+cosα/sinα-cosα=5 then sinα=?

Answer 1

sinA + cosA / sinA - cosA = 5
then,
sinA + cosA = 5sinA - 5cosA
sinA = 5sinA - 6cosA
6sinA - 6cosA = 0
sinA - cosA = 0
sinA = cosA

Answer 2

Answer:

$\sin\alpha=\dfrac{3}{\sqrt{13}}$

Step-by-step explanation:

We have been given the relation:-

$\dfrac{\sin\alpha+cos\alpha}{\sin\alpha-\cos\alpha}=5$

Cross multiply the equation:-


$(\sin\alpha+\cos\alpha)=5(\sin\alpha-\cos\alpha) \\ \\\sin\alpha+\cos\alpha=5\sin\alpha-5\cos\alpha \\ \\6\cos\alpha=4\sin\alpha \\ \\\tan\alpha = \dfrac{3}{2}$

The tangent function for a triangle is the ratio of Perpendicular over Base.

For a triangle, with its Base as 2 units and Perpendicular as 3 units.

This triangle will have its Hypotenuse as:-

$H = \sqrt{{Base}^{2}+{Perpendicular}^{2}} \\ \\H = \sqrt{3^2+2^2} \\ \\H = \sqrt{13} \ units$

The Sine function for a triangle is the ratio of Perpendicular over Hypotenuse.

Therefore,

$\sin\alpha=\dfrac{Perpendicular}{Hypotenuse} \\ \\ \sin\alpha=\dfrac{3}{\sqrt{13}}$